The present invention pertains generally to devices that are useful for separating particles (ions) of a predetermined mass from other charged particles in a multi-species plasma. More particularly, the present invention pertains to devices that accelerate selected particles (ions) at their cyclotron frequencies by using a resonant electric field to segregate and separate the selected ions from the plasma. The present invention is particularly, but not exclusively, useful for employing a stochastically generated electric field, having a predetermined band of frequencies, that will resonate with selected particles having respective cyclotron frequencies within the band of frequencies to thereby separate the selected particles from other charged particles in a plasma.
Cyclotron resonance occurs under conditions wherein electromagnetic power is coupled into a system of charged particles. The consequence of this coupling is a phenomenon known as ion cyclotron resonance heating (ICRH). Simply stated, ICRH occurs when a charged particle (e.g. an ion) is positioned in a uniform magnetic field, and the frequency of the electromagnetic power is resonant with the cyclotron frequency of the charged particle. The result is that the charged particle is accelerated into a spiral path by the absorption of energy from the electromagnetic power.
In a basic cyclotron, the charged particles are accelerated by electromagnetic waves having a fixed frequency. It happens, however, that the maximum ion energy that can be attained using a fixed frequency is limited because there is a relativistic mass increase for the ions at very high energies. This increase in mass then breaks the synchronous relationship for resonance between the frequency of the electromagnetic power and the cyclotron frequency of the charged particles. To overcome this difficulty, the synchrocyclotron was invented to modulate the electromagnetic power, and to thereby compensate for the relativistic mass increase. The dynamic modulation of electromagnetic power that is required to maintain an operation that is synchronous with relativistic mass increases can, however, be problematical. Consequently, the stochastic cyclotron was invented to effectively make such an operation steady state. In essence, a stochastic cyclotron is able to provide random inputs, within a specified frequency range, which will statistically accelerate ions in the stochastic cyclotron so long as the relativistic mass increases and the consequent cyclotron frequencies of the ions remain within the range.
Insofar as plasma mass filters are concerned, it is known that the basic principles of ICRH can be applied to a multi-species plasma to separate charged particles of a selected mass from other particles in the plasma. For example, such a procedure is disclosed in U.S. Pat. No. 5,442,481, which issued to Louvet on May 13, 1994 for an invention entitled xe2x80x9cDEVICE FOR ISOTOPE SEPARATION BY ION CYCLOTRON RESONANCE.xe2x80x9d Also an exemplary plasma mass filter has been recently disclosed by Ohkawa in U.S. Pat. No. 6,096,220 issued on Aug. 1, 2000 for an invention entitled xe2x80x9cPLASMA MASS FILTER.xe2x80x9d This invention separates particles based on the magnitude of their mass charge ratio. Using this technology, it may sometimes be desirable to isolate and separate a group of charged particles that have nearly the same mass numbers. For instance, in one application it would be desirable to remove transuranic elements or fission fragments from nuclear waste. In this case the transuranic elements have mass numbers in the range of 235 to 240 and the fission fragments will have mass numbers in the range of 80 to 120. Most of the non-radioactive material will have mass numbers less than 60. In such a situation, it may be desirable to remove all of the particles having mass numbers in the range of 235 to 240 as well as particles having mass numbers in the range of 80 to 120. The mathematical development which describes how this condition can be realized is helpful.
In describing the acceleration of the ions, consider an example where the electric field Ex is uniform and in x-direction. (The static magnetic field is in z-direction.) The time dependence is given by                               E          x                =                              ∫                          ω              ⁢              1                                      ω              ⁢              2                                ⁢                                    F              ⁡                              [                ω                ]                                      ⁢            cos            ⁢                          xe2x80x83                        ⁢            ω            ⁢                          xe2x80x83                        ⁢            t            ⁢                          ⅆ              ω                                                          (                  Eq          .                      xe2x80x83                    ⁢          1                )            
where F is the Fourier component. We choose the white noise spectrum between the frequencies xcfx891 and xcfx892, i.e.
F[xcfx89]=F xcfx892xe2x89xa7xcfx89xe2x89xa7xcfx891
F[xcfx89]=0 xcfx89 greater than xcfx892 and xcfx89 less than xcfx891xe2x80x83xe2x80x83(Eq. 2)
The equations of the motion of the ions are given by
Mdvx/dt=evyB+eEx
Mdvy/dt=xe2x88x92evx
Mdvz/dt=0xe2x80x83xe2x80x83(Eq. 3)
where M is the mass of the ions and B is the static magnetic field. We define u by
u=exp [ixcexa9t][vx+ivy]
where xcexa9=eB/M, and obtain                     u        =                                            [                                                e                  /                  2                                ⁢                                  xe2x80x83                                ⁢                i                ⁢                                  xe2x80x83                                ⁢                M                            ]                        ⁢                                          ∫                                  ω                  ⁢                  1                                                  ω                  ⁢                  2                                            ⁢                                                                    F                    ⁡                                          [                      ω                      ]                                                        ⁢                                      xe2x80x83                                    [                                                                                                              {                                                                                    exp                              ⁡                                                              [                                                                                                      i                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    Ω                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    t                                                                    +                                                                      i                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    ω                                                                                                  ]                                                                                      -                            1                                                    }                                                ⁡                                                  [                                                      Ω                            +                            ω                                                    ]                                                                                            -                        1                                                              +                                                                                            {                                                                                    exp                              ⁡                                                              [                                                                                                      i                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    Ω                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    t                                                                    -                                                                      i                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    ω                                    ⁢                                                                          xe2x80x83                                                                        ⁢                                    t                                                                                                  ]                                                                                      -                            1                                                    }                                                ⁡                                                  [                                                      Ω                            -                            ω                                                    ]                                                                                            -                        1                                                                              ]                                ⁢                                  ⅆ                  ω                                                              +                      u            0                                              (                  Eq          .                      xe2x80x83                    ⁢          4                )            
where the subscript 0 denotes the value at t=0.
The first term does not contain the resonance term and is neglected. The resonant part with F[l] given by Eq. 2 becomes                     u        =                                            [                              e                ⁢                                  xe2x80x83                                ⁢                                  F                  /                  2                                ⁢                i                ⁢                                  xe2x80x83                                ⁢                M                            ]                        ⁢                                          ∫                                  ω                  ⁢                  1                                                  ω                  ⁢                  2                                            ⁢                                                                                          {                                                                        exp                          ⁡                                                      [                                                                                          i                                ⁢                                                                  xe2x80x83                                                                ⁢                                Ω                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                            -                                                              i                                ⁢                                                                  xe2x80x83                                                                ⁢                                ω                                ⁢                                                                  xe2x80x83                                                                ⁢                                t                                                                                      ]                                                                          -                        1                                            }                                        ⁡                                          [                                              Ω                        -                        ω                                            ]                                                                            -                    1                                                  ⁢                                  ⅆ                  ω                                                              +                      u            0                                              (                  Eq          .                      xe2x80x83                    ⁢          5                )            
The above expression can be written in terms of Sine integral Si and Cosine integral Ci,
u=[eF/2M]{{Si[xcfx892txe2x88x92xcexa9t]+Si[xcexa9txe2x88x92xcfx891t]+
i{Ci[xcfx892txe2x88x92xcexa9t]+Ci[xcexa9txe2x88x92xcfx891t]xe2x88x92
1n[xcex3{xcfx892xe2x88x92xcexa9}t]xe2x88x921n[xcex3{xcexa9xe2x88x92xcfx891}t]}}+
u0xe2x80x83xe2x80x83(Eq. 6)
where xcex3=1.781.
For small values of the argument, consider
Si["xgr"]xe2x86x92"xgr"
and
xe2x80x83Ci["xgr"]xe2x86x921n[xcex3"xgr"]
and obtain
u≈[eF/2M][xcfx892xe2x88x92xcfx891]txe2x80x83xe2x80x83(Eq. 7)
where u0=0 is assumed.
The electric field strength E is given by
E=[xcfx892xcfx891]F
and Eq. 7 becomes
u≈[eE/2M]txe2x80x83xe2x80x83(Eq. 8)
In the asymptotic limit,
Si["xgr"]xe2x86x92xcfx80/2xe2x88x92cos "xgr"/"xgr"
Ci["xgr"]xe2x86x92sin "xgr"/"xgr"
By neglecting the logarithmic terms we obtain
u xe2x86x92[eF/2M]xcfx80=[eE/2M]xcfx80[xcfx892xe2x88x92xcfx891]xe2x88x921xe2x80x83xe2x80x83(Eq. 9)
The velocities given by Eq. 8 and Eq. 9 show that the ions are accelerated initially at the rate equal to that for the single frequency resonance and the acceleration saturates after xcexa9/{2[xcfx892xe2x88x92xcfx891]} cyclotron cycles.
When the frequency interval xcfx891 to xcfx892 does not contain the cyclotron frequency xcexa9, i.e.
xcexa9 less than xcfx891 less than xcfx892 or xcexa9 greater than xcfx892 greater than xcfx891
the real part of the velocity given by Eq. 1 becomes
Reu=[eF/2M]{Si[xcfx892txe2x88x92xcexa9t]xe2x88x92Si[xcfx891txe2x88x92xcexa9t]} xcexa9 less than xcfx891 less than xcfx892xe2x80x83xe2x80x83(Eq. 10)
or
=[eF/2M]{Si[xcexa9txe2x88x92xcfx891t]xe2x88x92Si[xcexa9txe2x88x92xcfx892t]} xcexa9 greater than xcfx892xcfx891
In either case,
Reuxe2x86x920 for txe2x86x92∞
The above expression shows that the acceleration does not occur unless the frequency interval contains the cyclotron frequency.
Another consequence of the mathematical development presented above is that a stochastic acceleration is tolerant of the stochasticity resulting from collisions between ions as they are being accelerated. This is in contrast with a typical cyclotron operation which uses a single fixed frequency to establish cyclotron resonance. In the case of the typical cyclotron (fixed frequency), collisions between both resonant and nonresonant ions will interrupt the synchronous (resonant) relationship between the input frequency of the electromagnetic power and the cyclotron frequency of the accelerated ions. Due to these collisions, the performance of the typical cyclotron is degraded. On the other hand, with a stochastic electromagnetic input, there is sufficient bandwidth to accelerate several ion species so long as the ions are in the appropriate range of masses. Further, any collisions that may occur between accelerated ions will not interfere with the acceleration as long as the collisional frequency of the ions (xcexd) does not exceed the bandwidth (xcfx892xe2x88x92xcfx891) of the stochastic electromagnetic input (xcfx892xe2x88x92xcfx892xe2x89xa7xcexd). A consequence of this is the possibility for a higher throughput.
In light of the above, it is an object of the present invention to provide a stochastic cyclotron ion filter that can selectively isolate and separate ions from a multi-species plasma that have mass numbers that are within a predetermined range of values. Yet another object of the present invention is to provide a stochastic cyclotron ion filter that can be operated to achieve a higher throughput. Still another object of the present invention is to provide a stochastic cyclotron ion filter that is relatively easy to manufacture, is easy to use, and is comparatively cost effective.
In accordance with the present invention, a stochastic cyclotron ion filter requires crossed electric and magnetic fields (Exc3x97B), wherein the electric field has RF electromagnetic power that results from using a stochastic input. More specifically, the stochastic input is generated by a white noise source, and a band pass filter that is connected with the noise source. As intended for the present invention, the band pass filter passes only those frequencies in the noise that are within a predetermined frequency interval, i.e. all frequencies that are in the bandwidth between a first frequency (xcfx891) and a second frequency (xcfx892). An amplifier is also provided, and is connected to the band pass filter to strengthen frequencies in the frequency interval.
In combination with the stochastic input, the present invention includes a substantially cylindrical shaped chamber that is provided to receive a multi-species plasma from a plasma source. The chamber defines a longitudinal axis and has a plurality of magnetic coils that are positioned around the chamber. Specifically, these magnetic coils are oriented in planes substantially perpendicular to the axis, in order to establish an axially oriented, uniform magnetic field (B) inside the chamber. Also, an oscillating electric field (E) is generated and oriented substantially perpendicular to the magnetic field to establish the crossed electric and magnetic fields (Exc3x97B) inside the chamber. Depending on the particular embodiment chosen for the present invention, a stochastic RF electric field can be generated inside the chamber in either of several ways.
For one embodiment of the present invention, an electrode (e.g. a plurality of concentric ring electrodes) is mounted at one end of the cylindrical chamber and is connected with the amplifier of the stochastic input. With this connection, the frequencies of the RF electric field will include all frequencies in the frequency interval that is passed by the band pass filter. In variations of this embodiment, an electrostatic electric field can also be established by any other means well known to the skilled artisan.
In another embodiment of the present invention, an additional electromagnetic coil can be positioned around the chamber to superpose an additional magnetic field onto the uniform magnetic field (B) in the chamber. This electromagnetic coil can then be connected with the amplifier and activated with frequencies in the frequency interval to induce an electric field in the chamber. It is to be appreciated that, if desired, only selected portions of the chamber need to be influenced by the electromagnetic coil. Thus, the effect of the stochastic cyclotron ion filter can be localized.
Regardless of how the RF electromagnetic field is generated for the present invention, it is preferable that the particles to be collected from the multi-species plasma have a collisional frequency (xcexd) inside the chamber that satisfies the condition xcfx892xe2x88x92xcfx891xe2x89xa7xcexd. Under this condition, more charged particles having a cyclotron frequency xcexa9within the frequency interval (xcfx891 less than xcexa9 less than xcfx892) will be selectively accelerated into large orbital paths in the chamber. The selectively accelerated particles can then be separated from the background ions and collected.